Subsidy design in a vessel speed reduction incentive program under government policies

As a green port and shipping-related policy, the vessel speed reduction incentive program (VSRIP) involves using a subsidy to induce ships to reduce their speed in a port area so that the emissions can be reduced at the port. However, this program may attract new ships to visit the port because of the subsidy; in this case, the port's profit will grow due to more ship visits, but its total emissions may also increase, which is counter to the original intention of the subsidy. The government could then intervene by providing part of the subsidy for the VSRIP or by collecting air emission taxes for the increased emission at the port. This paper studies how to design suitable subsidies for ships participating in a VSRIP. Two bilevel subsidy design models are formulated based on a Stackelberg game to maximize the port's profit (related to the profits from original and new ships, the subsidy provided by the port, and air emission taxes) and to minimize the government's cost (related to the damage cost of air emissions, the subsidy provided by the government, and air emission taxes). We determine which policy (including a sharing subsidy policy, no government intervention, and an air emission tax policy) should be implemented by the government in different cases and how much subsidy should be provided by the port under each government policy. We find that these decisions are affected by several practical factors, such as the damage cost of air emissions per ton of fuel and the subsidy sensitivities of original and new ships. We also outline several meaningful insights based on the analysis of these practical factors.